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Joel Jacobs wrote-

>I do
>have "Stability and Trim for the Ship's Officer" by La Dadge and Van Gemert
>handy.
>
>On page 35, they move beyond the standard formula Henry presents to the
>following:
>
>Saying "moment of inertia is a difficult term to define simply." and "This
>moment which resists motion of an infinite number of moments which are
>composed of the product  of each elementary area and the square of the
>distance from the axis." (simple?)
>
>I = L x B3 / 12 for a rectangular waterplane
>
>For non-rectangular waterplanes I = L x B3 x k
>
>k is a constant that relates to a waterplane coefficient
>
>They conclude that the moment of inertia "is almost wholly dependent on
>breadth of the vessel."

=================

This is a bit misleading. They are referring to the moment of inertia of a
thin flat waterplane, about a fore-and-aft axis, such as a raft (if it can
be said to have a fore-and-aft axis). They assume a constant "surface
density": that is, assume that the weight per surface are of the raft stays
constant when other dimensions are changed.

Robert Gainer was describing a rather different situation, in which the
dimensions of a vessel (which could well be a raft) are ALL scaled up in
proportion. So, as the breadth of a raft is increased by a certain ratio,
so is its length increased by that same ratio, and so is the depth
(vertical thickness) of the raft. And so, therefore , is its weight per
surface area.

Now the moment of inertia of the raft about a fore-and-aft axis is
proportional to length x (breadth)cubed x depth. So if you double all the
dimensions of that raft, you increase the moment of inertia, about its
fore-and-aft axis, by 2x2x2x2x2, the fifth power of 2, which is a factor of
32.

Note that before you specify a moment of inertia, you have to specify the
axis about which the rotation being considered is going to occur. The
moments of inertia about different axes will be very different. But in all
cases, when the dimensions of a vessel are all multiplied up by the same
factor (so that its shape doesn't change), the value of any moment of
inertia will change by that factor to the fifth power (i.e. multiplied by
itself 5 times). That's what Robert Gainer was pointing out.

George.

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